Proceedings of the American Mathematical Society

Rigidity of surfaces whose geodesic flows preserve smooth foliations of codimension 1

Author(s): José Barbosa Gomes; Rafael O. Ruggiero
Journal: Proc. Amer. Math. Soc. 135 (2007), 507-515.
MSC (2000): Primary 53C24; Secondary 53C22, 57R30, 37D40
Posted: August 28, 2006
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Abstract: Let

be a closed orientable surface. Assume that there exists a codimension one foliation $\mathcal F$ of class

in the unit tangent bundle of

, whose leaves are invariant under the geodesic flow of

. Then, the curvature of

is a nonpositive constant.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C24, 53C22, 57R30, 37D40

José Barbosa Gomes
Affiliation: Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil, 36036-330
Email: jbarbosa@ice.ufjf.br

Rafael O. Ruggiero
Affiliation: Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, Brazil, 22453-900
Email: rorr@mat.puc-rio.br

DOI: 10.1090/S0002-9939-06-08755-7
PII: S 0002-9939(06)08755-7
Keywords: Godbillon-Vey number, geodesic flow, rigidity, Anosov flow
Received by editor(s): September 14, 2005
Posted: August 28, 2006
Additional Notes: The first author was supported in part by CAPES of the Brazilian Government.
The second author was supported in part by CNPq of the Brazilian Government
Communicated by: Michael Handel
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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